1. Field of the Invention
The present invention relates to an S-parameter calculation technology used to design a high-frequency circuit and so on, and more particularly, to an apparatus and method for S-parameter calculation, and program and recording medium thereof, capable of accurately calculating S-parameters of an entire system made up of a plurality of devices and calculating S-parameters of arbitrary lengths of a single device having a large aspect ratio such as a cable or wiring.
2. Description of the Related Art
First, S-parameters will be explained. S-parameters are parameters indicating a relationship between inputs and outputs of a circuit. When there is an input from a port 1 of a circuit with 4 port terminals as shown in FIG. 13, outputs corresponding to certain characteristics appear at respective ports from port 1 to port 4. These characteristics are reflection for the port 1, transmission for the port 3 and crosstalk for the port 2 and port 4.
The relationship between the input and outputs of transmission, reflection and crosstalk of the circuit shown in FIG. 13 can be expressed in a form of a matrix calculation shown in FIG. 14. The matrix elements (S11 to S44) of the matrix (complex matrix) in FIG. 14 expressing the relationship between the input and output of the circuit are S-parameters. To be exact, S-parameters indicate relationships between absolute values of voltages and phases among ports.
Inputs/outputs of a circuit with 4 port terminals shown in FIG. 15 will be explained as an example. In the figure, suppose numerals 1 to 4 attached to the respective ports denote port numbers and ai (1≦i≦4) denotes an input from each port and bi (1≦i≦4) denotes an output of each port.
The relationship between inputs and outputs of the circuit with 4 port terminals shown in FIG. 15 can be expressed by a complex matrix whose matrix elements consist of S-parameters S11 to S44 as:
      (                                        b            1                                                            b            2                                                            b            3                                                            b            4                                )    =            (                                                  S              11                                                          S              12                                                          S              13                                                          S              14                                                                          S              21                                                          S              22                                                          S              23                                                          S              24                                                                          S              31                                                          S              32                                                          S              33                                                          S              34                                                                          S              41                                                          S              42                                                          S              43                                                          S              44                                          )        ⁢          (                                                  a              1                                                                          a              2                                                                          a              3                                                                          a              4                                          )      
S-parameters can be extracted through a three-dimensional electromagnetic field analysis and actual measurement. A transmission analysis using S-parameters is performed using SPICE which is a general circuit simulation tool. SPICE performs a transmission analysis by incorporating input S-parameters.
When S-parameters of an entire system to which a plurality of devices are connected are calculated, attempting to extract S-parameters by regarding the entire system as a simulation target using a technique based on a three-dimensional electromagnetic field analysis would cause the simulation scale to become too large to calculate S-parameters. Therefore, the technique based on the three-dimensional electromagnetic field analysis involves a problem that it is not possible to extract S-parameters of the entire system at a time.
For example, as shown in FIG. 16, when a system which comprises an LSI 110, a BGA (Ball Grid Array) 111, a connector 112, a BP (back panel) 113, a Via (not shown) provided for the BP 113, a PCB (printed circuit board) 114 and wiring 115 are subjected to a three-dimensional electromagnetic field analysis, the number of meshes and a calculation time increase, and therefore it is not possible to extract S-parameters of the entire system at a time.
Furthermore, S-parameters of a device having a large aspect ratio such as wiring or a cable as shown in FIG. 17, for example, cannot be extracted through a three-dimensional electromagnetic field analysis with sufficient accuracy and should be actually measured every time the length of the wiring or cable and so on is changed.
On the other hand, in the case of the technique based on actual measurements, as shown in FIG. 18, for example, when measuring systems 210 such as probes are attached on and beneath a connector 112 to measure S-parameters of the connector 112, S-parameters including not only the S-parameters of the connector 112 but also the S-parameters of the measuring systems 210 are measured, causing a problem that the accuracy in extracting S-parameter of the connector 112 itself degrades.
Furthermore, there is another problem that it is difficult to measure S-parameters of a device having a large aspect ratio such as a cable or wiring.
As shown above, it has been conventionally difficult to calculate S-parameters of an entire system made up of a plurality of devices, and therefore when carrying out a transmission analysis of the entire system, the conventional technology performs a transmission analysis by extracting S-parameters of single devices individually and connecting the extracted S-parameters on a SPICE model.
For example, the conventional technology performs a three-dimensional electromagnetic field analysis on the LSI 110, BGA 111, wiring 115 and connector 112 shown in FIG. 16 separately, extracts S-parameters device by device, connects the S-parameters of the respective devices on a SPICE model as shown in FIG. 19 and performs a transmission analysis of the entire system as shown in FIG. 16.
By using FIG. 20A, FIG. 20B and FIG. 21, the conventional technology will be explained more specifically. Suppose S-parameters of a test coupon 211 as shown in FIG. 20A are extracted and a transmission analysis using SPICE is performed. In FIG. 20A, reference numeral 212 denotes a probe and 115 denotes wiring. FIG. 20B is a cross-sectional view of the test coupon 211 shown in FIG. 20A. The notation “SUS” of the test coupon 211 shown in FIG. 20B denotes a stainless steel portion.
As shown in FIG. 20A, the S-parameter extraction target range corresponds to the portion having a length of 4 cm which corresponds to the wire length of the wiring 115. Since the S-parameter extraction target range is long, it is not possible to realize a three-dimensional electromagnetic field analysis as a single model. Therefore, the test coupon 211 is divided into two areas; left portion and right portion and S-parameters of the respective areas are extracted.
FIG. 21 illustrates a principle of the conventional technology. Of the divided test coupon 211, S-parameters of the left portion and S-parameters of the right portion are extracted individually through a three-dimensional electromagnetic field analysis. Then, SPICE models are created from the extracted S-parameters of the left portion and S-parameters of the right portion respectively and both SPICE models are connected and subjected to a transmission analysis.
There is no document describing a technology for carrying out a transmission analysis of an entire system which automatically calculates S-parameters of the entire system using connection codes based on a plurality of S-parameters, obtains S-parameters of the entire system and then creates a SPICE model.
When a transmission analysis is performed using the conventional technology, inverse FFT (Fast Fourier Transform) shown in Formula 1 below is performed as many times as the number of S-parameters connected on the SPICE model.
                              Y          ⁡                      (            t            )                          =                              ∫                          -              ∞                        t                    ⁢                                    S              ⁡                              (                τ                )                                      ⁢                          x              ⁡                              (                                  t                  -                  τ                                )                                      ⁢                          ⅆ              τ                                                          Formula        ⁢                                  ⁢        1            Formula 1 can be expressed as shown in Formula 2 in discrete areas.
                              Y          ⁡                      (                          n              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              t                        )                          =                              ∑                          k              =                              -                                  (                                      N                    -                    1                                    )                                                      0                    ⁢                                    S              ⁡                              (                                  k                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  t                                )                                      ⁢                          x              ⁡                              (                                                      (                                          n                      -                      k                                        )                                    ⁢                  Δ                  ⁢                                                                          ⁢                  t                                )                                                                        Formula        ⁢                                  ⁢        2            
Since the conventional technology connects S-parameters on a SPICE model and performs the integral calculation in Formula 2 repeatedly, errors may be accumulated producing so many errors that affect a transmission analysis. Therefore, it is difficult to perform an accurate transmission analysis.
FIG. 22 shows results of a transmission analysis conducted on the test coupon 211 shown in FIG. 20A by extracting S-parameters of the test coupon on the left portion and right portion as shown in FIG. 21 using the conventional technology and by creating SPICE models from the respective S-parameters. A thin line in the figure shows a measured value and a thick line shows the result of the transmission analysis using SPICE. As shown in the area encircled with a dotted line in FIG. 22, when a SPICE transmission analysis is performed using the conventional technology, it is observed that errors (disturbances of waveform) have occurred.
Furthermore, the conventional technology cannot calculate S-parameters of arbitrary lengths from some S-parameters of a single device having a large aspect ratio such as a cable or wiring.